You should be suspicious of Charles Saatchi's grandiose claims, especially since some artists in his new show are worthless. But the boldness of his vision deserves high praise, says Tom Lubbock

Art, like anything, lives on legends. The stories are told and retold and eventually turn into history. Of course you can believe them if you want to. It often makes things simpler. But not believing them can be fun too.

So how about this one? In the middle of last year it was widely reported that there were going to be some changes in the art world. The 1990s had seen the triumph of Britart. An art of rude, bright toys had made the running. The poor old art of painting was nowhere to be seen. It was certainly not the kind of thing to be found in that most fashionable art venue, the Saatchi Gallery, power base of Britart. And the news was that Charles Saatchi - setting the trend as ever - had changed his mind.

In 2005, the celebrated Iraqi/British collector would be reviving the cause of painting. He would be bringing a new batch of painters to the world's attention with a series of exhibitions called The Triumph of Painting. Part One opens tomorrow. Its title makes a clear bid for legend. It sounds like a chapter in a history book already. So, to start with, let's put the record straight. All the above story is untrue.

Whenever you hear about a revival of painting you should be suspicious. Modern painting is rather like modern religion. It is continually being declared dead and then suddenly it's reviving. Painting today is pretty well kept going by the question of its disputed mortality. Every few years, another twitch. But are these twitches signs of life? Or are they terminal spasms, or post-mortem effects, or even the symptoms of a strange, "undead", zombie half-life?

That's the big, ongoing, unanswerable question. (Personally I incline to the last option.)

And just at the moment painting is a highly fashionable art form. It's having a bout of serious twitches. In the past few years I can think of several major exhibitions that have identified a new spirit in painting (About Painting in Oxford, Examining Pictures at the Whitechapel Gallery, Hybrids in Tate Liverpool), and there have been many other smaller ones.

Or go round the trendy commercial galleries in London. Painting is currently so fashionable, it's on the verge of being unfashionable again.

What's more, the Saatchi Gallery itself - at both its former address in north London and its present address on the South Bank - has shown plenty of contemporary painting. And then, of the six painters showing in the Triumph of Painting: Part One, five are perfectly established names, widely shown elsewhere. One, Luc Tuymans, had a retrospective at Tate Modern last year.

As for the other half of the story, the alleged death of Britart, well, that's another bit of news that's been touted many times over the past 10 years. Does this mean the end of Britart?, someone urgently asks at the Turner Prize each year.

Depends what you mean, obviously. If Britart means an energetic bunch of work produced around the beginning of the 1990s, then obviously that has had its moment. But if you mean: will artists stop using found and fabricated objects and installations and video and all that stuff, and pick up their paintbrushes, then no they won't, not all of them.

To get a bit of perspective on the whole issue, consider this statistic. The 1997 Saatchi exhibition at the Royal Academy, Sensation, is generally taken as a kind of official monument to the Britart movement. In that show, more than a third of the artists were painters. Two-fifths. Confused? You must have been trying to believe the legends.

There is some real news here for the gallery-goer. The whole Saatchi Gallery is now given over to painting. This means that the centrepiece of its previous exhibitions, the crowd-pulling icons of Britart, the bed, the shark, the tent, the dead dad, the frozen blood head, the giant anatomical model, all these toys have been put away. (Damien Hirst's shark has been sold to America. Rachel Whiteread's plaster-cast room has left the collection too. Tracey Emin's tent - and it's still not clear how much else - was burnt in last year's warehouse fire.)

Since it moved to the old County Hall building two years ago, the Saatchi Gallery has been partly operating as a mausoleum to that eye-catching moment in British art. This role, presumably, it won't be playing any more.

If what you mean by the end of Britart is a waning of interest in Britart, I suppose not having its star-works in the same collection may well make a difference.

Meanwhile, throughout this year, all the ugly, wood-panelled, municipal spaces of the building are occupied by paintings. In fact the woodwork is a bit less visible than it was before. There's more white-walling, covering it over. (It was not so long ago that Saatchi was declaring the end of the white-walled contemporary art gallery. But that legend never quite took off.)

Each painting is given a good deal of space, sometimes a whole room to itself. The paintings are generally on the large side.

But are they any good? That's the real question of course. After all the soundings about painting generally, or Britart generally, it's always going to come down to something more specific.

You find yourself standing in front of a particular work by a particular artist. Will you be staying, or will you be moving rapidly on?

The six painters in the exhibition are the Austrian Hermann Nitsch, the Germans J?rg Immendorff and Martin Kippenberger, the South African-Dutch Marlene Dumas, the Belgian Luc Tuymans and the Canadian-Briton Peter Doig.

It's a funny kind of group show. The paintings don't really go together. In fact you might say they were extremely ill-assorted. And some of them are really pretty worthless.

Hermann Nitsch (born 1938), the Viennese Actionist, famous for his gory ritualistic performances, involving blood, nudity and dead animals, has produced (as a kind of by-product) a series of splatter paintings, canvasses drenched in violent washes and dribbles of red and brown paint, suggesting blood-letting. It looks like it means murder, but it turns out rather decorative, a succession of pretty messes, not paintings really, but you could put them on the wall and they'd settle down into a lively background.

J?rg Immendorff (born 1945) is another one for the scrapheap. He does these enormous, preposterously lurid and busy figurative paintings with neon colour-schemes. They look like much-magnified versions of the kind of illustration that would accompany a magazine article about mental illness.

The work of Martin Kippenberger (1953-1997) passes for humorous subversiveness in some parts of the art world. His paintings are immensely incompetent parodies of various different painting styles. His work is sustained by a jokey cult of personality, and I don't feel the pictures are even meant to be worth looking at. They're just a kind of adjunct to the act.

With Marlene Dumas (born 1953), things try to be more interesting. In these images of isolated human figures and faces, the painter is clearly up to something, after some sort of sensation, something painful, vulnerable, each paint mark feeling a little like a wound. And she gets it sometimes. The way she draws though, and you can't ignore it, is very slick and inert.

Luc Tuymans (born 1958) works a similar vein. Close-ups of barely emerging images, with the paint pale, weak, withdrawn, off-hand, half-hearted, they have - at their best - a captivating feebleness. One picture here has that. The down side, of course, is sheer feebleness (as in the vast still-life).

Peter Doig (born 1959) is the one solidly good painter here. His scenes are landscapes, woody or snowy, always partly obscured by the paint that pictures them. The paint is very dense and various and gorgeous, constantly changing tack, going thick and thin, weaving, blobbing, spraying. The colour world is extreme. The picture is an intense field of activity where every gesture is worth following.

Bizarre mix - but it's just what one person likes, isn't it. The Triumph of Painting? It makes the legendary title look silly, having such a flagrantly miscellaneous, capricious and uneven collection of work. But that's also what makes the show good. The Saatchi Gallery is a private gallery with more space and resources than many publicly funded galleries, but as a private gallery it's able to do the kind of bold, single-minded gesture that a Tate - with its duty to be representative and serious - can't do.

No self-respecting public gallery could put on a show like this, with no theme, no intellectual agenda, and a very rum load of stuff. But I wish curating went this way more often, out on a limb, not worrying about mockery, exposing the curator's taste nakedly to the world. It would take confidence, naturally. And I suppose nobody can ever feel quite as confident as a very, very rich man.

The Triumph of Painting: Part One - The Saatchi Gallery, County Hall, South Bank, London SE1; 26 January to 5 June. Open every day. Admission ?9, with concessions.